What is factor (5y-6)^2-81 ?

The solution to factor (5y-6)^2-81 is 5(5y+3)(y-3)

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factor (5y-6)^2-81

factor

(5 y - 6)^{2} - 81

5 (5 y + 3) (y - 3)

Solution steps

(5 y - 6)^{2} - 81

Factor the number:

81 = 9^{2}

= (5 y - 6)^{2} - 9^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(5 y - 6)^{2} - 9^{2} = ((5 y - 6) + 9) ((5 y - 6) - 9)

= ((5 y - 6) + 9) ((5 y - 6) - 9)

Simplify

((5 y - 6) + 9) ((5 y - 6) - 9) : (5 y + 3) (5 y - 15)

= (5 y + 3) (5 y - 15)

Factor

5 y - 15 : 5 (y - 3)

= (5 y + 3) \cdot 5 (y - 3)

= 5 (5 y + 3) (y - 3)

3 x^{2} y - 8 x^{4} y^{3} + 2 x^{5} y

\frac{3}{8} - \frac{11}{6}

\frac{1}{2} + \frac{7}{2} - 3 x = \frac{11}{9}

x (x - 12) = 0

\frac{2}{3} x - 2 = \frac{4}{6} x - 2